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On convex polyhedra as regular images of R(n)

Fernando Galván, José Francisco and Gamboa, J.M. and Ueno, Carlos (2011) On convex polyhedra as regular images of R(n). Proceedings of the London Mathematical Society , 103 . pp. 847-878. ISSN 0024-6115

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Abstract

We show that convex polyhedra in R(n) and their interiors are images of regular maps R(n) -> R(n). As a main ingredient in the proof, given an n-dimensional, bounded, convex polyhedron K subset of R(n) and a point p is an element of R(n) \ K, we construct a semialgebraic partition {A, B, T} of the boundary partial derivative K of K determined by p, and compatible with the interiors of the faces of K, such that A and B are semialgebraically homeomorphic to an (n - 1)-dimensional open ball and J is semialgebraically homeomorphic to an (n - 2)-dimensional sphere. Finally, we also prove that closed balls in R n and their interiors are images of regular maps R(n) -> R(n).

Item Type:Article
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:15062
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Deposited On:03 May 2012 09:16
Last Modified:06 Feb 2014 10:15

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